2,854 research outputs found
Non-linear Pattern Matching with Backtracking for Non-free Data Types
Non-free data types are data types whose data have no canonical forms. For
example, multisets are non-free data types because the multiset has
two other equivalent but literally different forms and .
Pattern matching is known to provide a handy tool set to treat such data types.
Although many studies on pattern matching and implementations for practical
programming languages have been proposed so far, we observe that none of these
studies satisfy all the criteria of practical pattern matching, which are as
follows: i) efficiency of the backtracking algorithm for non-linear patterns,
ii) extensibility of matching process, and iii) polymorphism in patterns.
This paper aims to design a new pattern-matching-oriented programming
language that satisfies all the above three criteria. The proposed language
features clean Scheme-like syntax and efficient and extensible pattern matching
semantics. This programming language is especially useful for the processing of
complex non-free data types that not only include multisets and sets but also
graphs and symbolic mathematical expressions. We discuss the importance of our
criteria of practical pattern matching and how our language design naturally
arises from the criteria. The proposed language has been already implemented
and open-sourced as the Egison programming language
ASMs and Operational Algorithmic Completeness of Lambda Calculus
We show that lambda calculus is a computation model which can step by step
simulate any sequential deterministic algorithm for any computable function
over integers or words or any datatype. More formally, given an algorithm above
a family of computable functions (taken as primitive tools, i.e., kind of
oracle functions for the algorithm), for every constant K big enough, each
computation step of the algorithm can be simulated by exactly K successive
reductions in a natural extension of lambda calculus with constants for
functions in the above considered family. The proof is based on a fixed point
technique in lambda calculus and on Gurevich sequential Thesis which allows to
identify sequential deterministic algorithms with Abstract State Machines. This
extends to algorithms for partial computable functions in such a way that
finite computations ending with exceptions are associated to finite reductions
leading to terms with a particular very simple feature.Comment: 37 page
Modelling the regulation of thermal adaptation in Candida albicans, a major fungal pathogen of humans
Peer reviewedPublisher PD
Relational Graph Models at Work
We study the relational graph models that constitute a natural subclass of
relational models of lambda-calculus. We prove that among the lambda-theories
induced by such models there exists a minimal one, and that the corresponding
relational graph model is very natural and easy to construct. We then study
relational graph models that are fully abstract, in the sense that they capture
some observational equivalence between lambda-terms. We focus on the two main
observational equivalences in the lambda-calculus, the theory H+ generated by
taking as observables the beta-normal forms, and H* generated by considering as
observables the head normal forms. On the one hand we introduce a notion of
lambda-K\"onig model and prove that a relational graph model is fully abstract
for H+ if and only if it is extensional and lambda-K\"onig. On the other hand
we show that the dual notion of hyperimmune model, together with
extensionality, captures the full abstraction for H*
Logic Programming and Logarithmic Space
We present an algebraic view on logic programming, related to proof theory
and more specifically linear logic and geometry of interaction. Within this
construction, a characterization of logspace (deterministic and
non-deterministic) computation is given via a synctactic restriction, using an
encoding of words that derives from proof theory.
We show that the acceptance of a word by an observation (the counterpart of a
program in the encoding) can be decided within logarithmic space, by reducing
this problem to the acyclicity of a graph. We show moreover that observations
are as expressive as two-ways multi-heads finite automata, a kind of pointer
machines that is a standard model of logarithmic space computation
Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality
We survey diverse approaches to the notion of information: from Shannon
entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov
complexity are presented: randomness and classification. The survey is divided
in two parts published in a same volume. Part II is dedicated to the relation
between logic and information system, within the scope of Kolmogorov
algorithmic information theory. We present a recent application of Kolmogorov
complexity: classification using compression, an idea with provocative
implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses
how Kolmogorov complexity, besides being a foundation to randomness, is also
related to classification. Another approach to classification is also
considered: the so-called "Google classification". It uses another original and
attractive idea which is connected to the classification using compression and
to Kolmogorov complexity from a conceptual point of view. We present and unify
these different approaches to classification in terms of Bottom-Up versus
Top-Down operational modes, of which we point the fundamental principles and
the underlying duality. We look at the way these two dual modes are used in
different approaches to information system, particularly the relational model
for database introduced by Codd in the 70's. This allows to point out diverse
forms of a fundamental duality. These operational modes are also reinterpreted
in the context of the comprehension schema of axiomatic set theory ZF. This
leads us to develop how Kolmogorov's complexity is linked to intensionality,
abstraction, classification and information system.Comment: 43 page
Generalized Communicating P Systems Working in Fair Sequential Model
In this article we consider a new derivation mode for generalized
communicating P systems (GCPS) corresponding to the functioning of population
protocols (PP) and based on the sequential derivation mode and a fairness
condition. We show that PP can be seen as a particular variant of GCPS. We also
consider a particular stochastic evolution satisfying the fairness condition
and obtain that it corresponds to the run of a Gillespie's SSA. This permits to
further describe the dynamics of GCPS by a system of ODEs when the population
size goes to the infinity.Comment: Presented at MeCBIC 201
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